Officers will not actively target members of the public to track down those who own violent pornography banned under a new law, police chiefs admitted yesterday.

The law, which comes into effect today, was passed in response to a three-year campaign by the mother of the teacher Jane Longhurst, who was murdered by a man obsessed with hardcore internet pornography.

Its aim, according to the government, is to protect the public from exposure to material which "should have no place in our society", and to tackle demand for such images in order to hit supply. On the internet these come almost exclusively from websites hosted abroad, over which Britain has no jurisdiction.

A Home Office-commissioned review of research into the effects of exposure to extreme pornographic material in 2007 found a correlation between the viewing of violent sexual images and pro-rape attitudes among the men surveyed.

But yesterday the justice ministry said it expected to see a only small number of prosecutions a year under the new law, which carries a maximum sentence of three years in jail and makes it illegal to own pornographic material that depicts necrophilia, bestiality or violence that looks life-threatening or is likely to result in serious injury to the breasts, genitals or anus.

Responsibility for implementing the ban will lie with individual police forces, which will receive no extra funding and will not be expected to devote resources to speculative hunts for people viewing extreme pornography.

The policy is in contrast with the investigation of the use of child pornography. At the Child Exploitation and Online Protection Centre in London, officers monitor file-sharing websites to try to work out who is accessing illegal material.

A statement from the Association of Chief Police Officers said: "The police will not be actively targeting members of the public but will be conducting investigations into the unlawful possession of this material where found."

The justice ministry expects to see about 30 prosecutions a year. It estimates that 10 offenders will be jailed, for an average of six months.

Women's organisations expressed concern that officers would not search for users of the material unless prompted by specific suspicions or other investigations.

Katherine Rake, director of the Fawcett Society, said: "It would make a nonsense of the legislation if there wasn't proactive policing around it."

Sandrine Leveque, of Object, which campaigns against the objectification of women, said: "Many women's organisations see this material as a factor in violence against women. For a law to have any effect there needs to be the feeling that you might be caught breaking it, and if that's not there it does undermine it."

Liz Longhurst believes her daughter Jane might not have been murdered by Graham Coutts had he not had access to extreme pornographic sites. He had been viewing images depicting strangulation and faked murder and rape before he killed the 31-year-old in 2003.

Longhurst, 77, said she had expected that the implementation of the law would lack teeth and resources, but hoped it would eventually lead to tougher policing of violent pornography.

"I think it will have a slight effect, but if it doesn't have a lot of effect it will concentrate the minds of people and possibly they will tighten the law," she said."